In large, introductory courses, instructors and teaching assistants often struggle to provide detailed feedback on student homework in a timely manner. Here we describe a peer-reviewed homework system that provides quick turnaround while offering flexibility in the construction of homework problems. Homework is administered through a cycle, which always consists of weekly peer-reviewed feedback on paper-based homework. The peer-review component has two purposes: (a) it provides students completing homework with detailed explanations of the correctness of their approach, and (b) it provides peer reviewers an opportunity to review other problem-solving strategies. By examining other students' strategies, peer reviewers gain greater insight into problem solving. We have tested this approach in a general chemistry class at a large institution and observed benefits for students and instructors. This article discusses peer-reviewed homework design and implementation, as well as the results obtained in a large-enrollment class.